How do technicians repair broken communications cables at the bottom of the ocean without actually seeing them? What's the likelihood of plucking a needle out of a haystack the size of the Earth? And is it possible to use computers to create a universal library of everything ever written or every photo ever taken? These are just some of the intriguing questions that best-selling popular math writer Paul Nahin tackles in Number-Crunching. Through brilliant math ideas and entertaining stories, Nahin demonstrates how odd and unusual math problems can be solved by bringing together basic physics ideas and today's powerful computers. Some of the outcomes discussed are so counterintuitive they will leave readers astonished.

Nahin looks at how the art of number-crunching has changed since the advent of computers, and how high-speed technology helps to solve fascinating conundrums such as the three-body, Monte Carlo, leapfrog, and gambler's ruin problems. Along the way, Nahin traverses topics that include algebra, trigonometry, geometry, calculus, number theory, differential equations, Fourier series, electronics, and computers in science fiction. He gives historical background for the problems presented, offers many examples and numerous challenges, supplies MATLAB codes for all the theories discussed, and includes detailed and complete solutions.

Exploring the intimate relationship between mathematics, physics, and the tremendous power of modern computers, Number-Crunching will appeal to anyone interested in understanding how these three important fields join forces to solve today's thorniest puzzles.

技术人员如何在没有实际看到的情况下修复海底破损的通信电缆？从地球那么大的干草堆中拔出一根针的可能性有多大？还有，是否有可能利用计算机创建一个包含所有曾经写过的东西或拍过的每张照片的通用图书馆？这些只是最畅销的流行数学作家保罗-纳欣在《数字计算》中解决的一些引人入胜的问题。通过精彩的数学思想和有趣的故事，纳欣展示了奇怪和不寻常的数学问题是如何通过将基本的物理学思想和当今强大的计算机结合起来解决的。所讨论的一些结果是如此的反直觉，会让读者大吃一惊。

纳欣研究了计算机出现后数字计算的艺术发生了怎样的变化，以及高速技术如何帮助解决迷人的难题，如三体、蒙特卡洛、跃迁和赌徒的毁灭问题。一路走来，纳欣穿越了包括代数、三角学、几何学、微积分、数论、微分方程、傅里叶级数、电子学和科幻小说中的计算机等主题。他介绍了所提出问题的历史背景，提供了许多例子和许多挑战，为所有讨论的理论提供了MATLAB代码，并包括详细和完整的解决方案。

探讨数学、物理学和现代计算机的巨大威力之间的密切关系，《数理化》将吸引任何对了解这三个重要领域如何联合起来解决当今最棘手的难题感兴趣的人。